Skunkatanka that’s simply not true.
There is growing evidence to support the view (long held, by many cultures and individuals) that co-sleeping when done correctly is the safest way for babies to sleep. There are lots of studies out there which can be easily accessed online if you care to read them, but here's just one excerpt from Ball & Russell's 2014 study into the links between SIDS and co-sleeping:
Researchers found that the incidence of co-sleeping among the SIDS infants was significantly higher than for the controls. However when results were broken down to specific co-sleeping environments, it was found that co-sleeping on a sofa, or next to a parent who had drunk more than two units of alcohol carried a very high risk. Co-sleeping next to a smoker was significant for infants under three months, whilst the risk associated with bed-sharing in the absence of these factors was not significant overall, and was in the direction of protection for older infants (over three months).
This study supports what many people have said for a long time, which is that co-sleeping gets a bad rep based on some people not following safe co-sleeping practices. Anecdotally, I've seen two articles in the last few months online regarding tragic baby deaths where the tone of the article was anti co-sleeping, containing several references to the anti co-sleeping NHS guidelines etc and the comments under the articles were all very much warning against sleeping with babies. One case was a father who had fallen asleep with his baby on the sofa and the baby had slipped down between him and the sofa back. The other case was a lady who was using a morphine patch and during the night the patch had detached from her and become stuck to the baby. Instances like this contribute to the negative opinions of the UK general public about co-sleeping. I've said it before on MN, but using these types of cases to warn against co-sleeping is akin to using a story about a drunk driver to warn everyone that driving cars is dangerous and none of us should do it. Co-sleeping is safe, as long as it's done properly.
OP, I have everything crossed that you both manage some sleep! I don't know how old your DC is, but I did find that it got easier as DD got older and the breastfeeding lying down definitely got way easier the bigger she got. Sometimes you've got to do what you've got to do. You are aware of safe co-sleeping guidelines which is a massive part of it (I.e. you're not going to do anything dangerous like stick a duvet on him or whatever). I think you have to weigh the risks of sleeping in a less-than-perfect position against the risks of being in sole charge of a baby when you're on your knees with exhaustion because you've not slept. Sleep is important. Obviously you minimise the risks as much as you possibly can (which you are doing) but none of us are perfect. We just get through as best we can!